A182470 -id:A182470 - cp's OEIS frontend

A182547 Decimal expansion of Pi^gamma, where gamma is the Euler-Mascheroni constant.

1, 9, 3, 6, 2, 5, 5, 6, 3, 3, 4, 1, 9, 6, 7, 4, 4, 6, 0, 0, 1, 3, 9, 3, 4, 6, 3, 8, 9, 4, 6, 3, 2, 9, 9, 6, 0, 2, 9, 1, 1, 6, 2, 0, 1, 4, 3, 0, 6, 5, 6, 5, 7, 9, 6, 3, 3, 3, 6, 2, 6, 6, 8, 2, 5, 1, 6, 6, 7, 2, 0, 5, 1, 1, 9, 9, 3, 7, 6, 7, 1, 0, 8, 5, 5, 2, 2, 7, 4, 8, 6, 7, 2, 4, 9, 9, 3, 8, 8, 5, 6, 3, 5, 8, 2

Offset: 1

Volker Werner, May 04 2012

			1.93625563341967446001393463894632996029116201430656...

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A000796, A001620, A182470.

R:= RealField(100); Pi(R)^EulerGamma(R); // G. C. Greubel, Sep 03 2018

RealDigits[ N[Pi^EulerGamma, 105]] [[1]]

default(realprecision, 100); Pi^Euler \\ G. C. Greubel, Sep 03 2018

Equals A000796^A001620.

A182496 Decimal expansion of 1/(gamma^Pi), where gamma is the Euler-Mascheroni constant.

Original entry on oeis.org

5, 6, 2, 0, 5, 4, 5, 1, 9, 2, 3, 8, 6, 3, 6, 7, 4, 3, 6, 5, 8, 4, 1, 7, 2, 0, 7, 1, 4, 1, 5, 9, 8, 8, 8, 6, 4, 1, 6, 2, 5, 0, 2, 8, 1, 2, 3, 9, 4, 3, 4, 5, 2, 7, 9, 1, 3, 8, 8, 6, 6, 7, 5, 4, 7, 5, 1, 9, 6, 7, 8, 1, 5, 2, 5, 1, 2, 2, 1, 7, 1, 7, 0, 5, 3, 0, 7, 1, 8, 9, 6, 1, 9, 0, 4, 8, 2, 9, 3, 4, 6, 6, 1, 9, 2

Offset: 1

Volker Werner, May 02 2012

			5.62054519238636743658417207141598886416250281239434...

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A000796, A001620, A182470.

R:= RealField(100); 1/(EulerGamma(R)^Pi(R)); // G. C. Greubel, Sep 06 2018

RealDigits[1/(EulerGamma^Pi),10,105][[1]]

default(realprecision, 100); 1/(Euler^Pi) \\ G. C. Greubel, Sep 06 2018

Equals 1/A182470.

A282471 First differences of A282470.

Original entry on oeis.org

0, 1, 8, 7, 24, 22, 40, 22, 80, 54, 80, 22, 80, 54, 112, 70, 240, 134, 144, 22, 80, 54, 112, 70, 240, 134, 176, 70, 240, 150, 336, 246, 720, 326, 272, 22, 80, 54, 112, 70, 240, 134, 176, 70, 240, 150, 336, 246, 720, 326, 304, 70, 240, 150, 336, 246, 720, 342, 464, 246, 752, 454, 1136, 838, 2064

Offset: 0

Omar E. Pol, Mar 17 2017

			Written as an irregular triangle the sequence begins:
0;
1;
8;
7;
24;
22, 40;
22, 80, 54, 80;
22, 80, 54, 112, 70, 240, 134, 144;
22, 80, 54, 112, 70, 240, 134, 176, 70, 240, 150, 336, 246, 720, 326, 272;
22, 80, 54, 112, 70, 240, 134, 176, 70, 240, 150, 336, 246, 720, 326, 304, 70,...
...
Starting from a(3) = 7 the row lengths of triangle are the terms of A011782.

Cf. A011782, A139251, A187210, A187211, A182470, A282470.

a(2n) = 2*A187211(2n).

a(2n+1) = A187211(2n+1).

A179947 Continued fraction for gamma^Pi.

Original entry on oeis.org

0, 5, 1, 1, 1, 1, 1, 2, 1, 7, 1, 1, 36, 2, 1, 1, 56, 2, 44, 1, 1, 1, 34, 3, 5, 1, 1, 1, 15, 3, 1, 2, 12, 2, 4, 2, 17, 4, 2, 1, 2, 2, 2, 1, 1, 1, 29, 6, 1, 4, 1, 3, 1, 1, 4, 3, 2, 1, 3, 1076, 17, 3, 49, 1, 2, 2, 2, 3, 20, 4, 13, 3, 2, 90, 1, 1, 2, 12, 2, 1, 3, 1, 7, 1, 10, 1, 2, 1, 2, 4, 206, 2, 2, 1, 6

Offset: 0

Michel Lagneau, Aug 03 2010

			gamma^Pi = 0.1779186832897647510663236... = 0 + 1/(5 + 1/(1 + 1/(1 + 1/(1 + ...)))).

K. Y. Choong, D. E. Daykin and C. R. Rathbone, Regular continued fractions for pi and gamma, Math. Comp., 25 (1971), 403.

Cf. A182470.

with(numtheory): Digits := 300: convert(evalf(gamma(0)^Pi), confrac);

ContinuedFraction[EulerGamma^Pi,100] (* Harvey P. Dale, Aug 19 2022 *)

contfrac(Euler^Pi) \\ Michel Marcus, Oct 11 2017

A342934 Decimal expansion of gamma^(1/gamma), where gamma is the Euler-Mascheroni constant.

Original entry on oeis.org

3, 8, 5, 9, 4, 8, 2, 5, 4, 7, 1, 9, 8, 4, 1, 0, 5, 8, 0, 3, 7, 3, 6, 5, 0, 0, 8, 1, 1, 7, 5, 3, 7, 2, 0, 8, 4, 5, 3, 5, 7, 1, 5, 6, 2, 5, 0, 1, 4, 0, 5, 9, 6, 5, 4, 6, 7, 6, 9, 4, 0, 5, 4, 1, 8, 1, 9, 6, 6, 5, 7, 5, 1, 5, 6, 3, 4, 3, 2, 0, 8, 8, 5, 2, 9, 2, 3, 5, 9, 9

Offset: 0

Christoph B. Kassir, Aug 30 2021

			0.385948254719841058037365008117537208453571562501405965467694054181966575...

Michael Ian Shamos, Shamos's catalog of the real numbers, (2011).

Cf. A001620, A098907, A345066, A346589, A073004, A182547, A182470, A073018.

Maple
```
Digits := 100; evalf(gamma^(1/gamma));
```

RealDigits[EulerGamme^(1/EulerGamma), 10, 100][[1]]

PARI
```
Euler^(1/Euler)
```

A348362 Decimal expansion of gamma^gamma, where gamma is the Euler-Mascheroni constant.

Original entry on oeis.org

7, 2, 8, 1, 8, 3, 1, 3, 7, 4, 9, 2, 5, 4, 3, 0, 4, 1, 1, 4, 9, 2, 1, 6, 9, 2, 7, 7, 9, 3, 4, 9, 0, 6, 1, 7, 2, 8, 9, 5, 5, 5, 9, 8, 0, 4, 2, 8, 1, 2, 0, 0, 6, 7, 8, 9, 8, 7, 7, 2, 3, 4, 5, 0, 6, 9, 3, 1, 9, 7, 5, 6, 3, 8, 1, 4, 4, 1, 7, 9, 9, 2, 9, 2

Offset: 0

Christoph B. Kassir, Oct 14 2021

			0.7281831374925430411492169277934906172895559804281200678987723450693...

Michael Ian Shamos, Shamos's catalog of the real numbers, (2011).

Cf. A001620, A345066, A346589, A073004, A182547, A182470, A073018.

R:= RealField(100); EulerGamma(R)^EulerGamma(R);

Maple
```
Digits := 100; evalf(gamma^gamma);
```

RealDigits[EulerGamma^EulerGamma, 10, 100][[1]]

PARI
```
Euler^Euler
```

cp's OEIS Frontend

A182547 Decimal expansion of Pi^gamma, where gamma is the Euler-Mascheroni constant.

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A182496 Decimal expansion of 1/(gamma^Pi), where gamma is the Euler-Mascheroni constant.

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A282471 First differences of A282470.

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A179947 Continued fraction for gamma^Pi.

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Maple

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A342934 Decimal expansion of gamma^(1/gamma), where gamma is the Euler-Mascheroni constant.

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Author

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Examples

Links

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Programs

Maple

Mathematica

PARI

A348362 Decimal expansion of gamma^gamma, where gamma is the Euler-Mascheroni constant.

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Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI